30.11.2021; Vortrag
Seminar Angewandte Mathematik - ArchivIan Tobasco: The many, elaborate wrinkle patterns of confined elastic shells
Abstract
A basic fact of geometry is that there are no length-preserving maps from the sphere to the plane. But what happens if you confine a naturally curved elastic shell nearby a plane? It wrinkles, forming a remarkable pattern of peaks and troughs, the arrangement of which is sometimes random, sometimes not depending on the shell. After a brief introduction to the mathematics of thin elastic sheets, this talk will focus on a set of simple, geometric rules we have discovered for predicting confinement-driven wrinkling. These rules are the latest output from an ongoing study of confinement problems in elasticity using the tools of Gamma-convergence and convex analysis. The asymptotic expansions they encode reveal a beautiful and unexpected connection between opposite curvatures - apparently, surfaces with positive or negative intrinsic Gaussian curvatures are paired according to the way that they wrinkle. Our predictions match the results of numerous experiments and simulations done with Eleni Katifori (U. Penn) and Joey Paulsen (Syracuse). Underlying their analysis is a certain class of interpolation inequalities of Gagliardo-Nirenberg type, whose best prefactors encode the optimal patterns.
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Link zur Veranstaltung: https://bbb.tu-dresden.de/b/sim-88d-3qd-uwz